This invention relates to musical instruments and more specifically to digitally controlled electronic instruments and methods for generating musical sound.
Digitally controlled methods of generating musical sound operate by producing a sequence of coded digital numbers which are converted to electrical analog signals. The analog signals are amplified to produce musical sound through a conventional speaker. Musical instruments which employ digital control are constructed with a keyboard or other input device and with digital electronic circuits responsive to the keyboard. The electronic circuits digitally process signals initiated by the keyboard and thereby digitally control the oscillations which form the sound in the speaker. These digitally controlled oscillations are distinguished from analog controlled oscillations generated by electronic oscillators and are distinguished from mechanically induced oscillations produced by conventional orchestral instruments.
All musical sounds, whether of electronic or mechanical origin, can be described by Fourier spectra. The Fourier spectra describes musical sound in terms of its component frequencies which are represented as sinusoids. The whole musical sound is therefore a sum of the component frequencies, that is, a sum of sinusoids.
Under Fourier analysis, tones are classified as harmonic or inharmonic. A harmonic tone is periodic and can be represented by a sum of sinusoids having frequencies which are integral multiples of a fundamental frequency. The fundamental frequency is the pitch of the tone. Harmonic instruments of the orchestra include the strings, the brasses, the woodwinds, the piano, and many more. An inharmonic tone is not periodic although it often can be represented by a sum of sinusoids. The frequencies comprising an inharmonic tone, however, usually do not have any simple relationship. Inharmonic instruments do not normally have any pitch associated with them. Instruments in the orchestra that are inharmonic include the percussion instruments, such as the base drum, the snare drum, and the cymbal and others.
Electronically controlled musical instruments have relied upon forming selected Fourier spectra as a basis for producing musical sound. One known type of digital musical instrument employs a harmonic summation method of music generation. In the harmonic summation method, a tone is produced by adding together a number of amplitude-scaled sinusoids of different frequencies. The harmonic summation method, however, requires a complex addition process to form each sample. That addition process requires digital circuitry which is both expensive and inflexible. Accordingly, the digital design necessary to carry out the method of harmonic summation leaves much to be desired.
Another known type of musical instrument employs the filtering method of music generation. In the filtering method, a complex electrical wave form, such as a square wave or a saw tooth pulse train, is filtered by one or more filters to select the desired frequency components. Thereafter, the filtered frequency components are combined to form the electrical signal which drives the speaker. The filtering method is commonly used to synthesize human speach and has often been used with analog electronic organs. The filtering method is comparatively expensive and inflexible since each sample cannot be produced independently of the previous sample and hence prior sample values must be stored. Also, the filtering method requires a large number of multiplication steps which are not economically performable.
Both the harmonic summation and the filtering methods rely upon a linear combination of sinusoids and hence they are characterized as linear methods. The linear property is apparent from the fact that multiplying the amplitude of the input function (sinusoids for harmonic summation or a pulse train for filtering) by a factor of two results in an output waveform with the same tone quality and with an amplitude multiplied by a factor of two.
The above cross-referenced Chowning application describes a non-linear method for electronically controlling the generation of musical sound. That nonlinear method employs a closed-form expression (based upon frequency modulation) to represent the sum of an infinite number of sinusoids. That non-linear frequency modulation method produces a number of sinusoids which have frequencies which are the sum of the carrier frequency and integral multiples of the modulation frequency. The amplitudes of the multiples of the modulation frequency, however, are constrained to be sums of Bessel functions.
While the non-linear frequency modulation method of Chowning is a significant improvement over the linear harmonic summation and filtering methods, improved methods of musical sound generation are still needed. For example, it is desirable to remove the requirement that the amplitudes of frequency components be constrained to the Bessel functions. Furthermore, it is desirable at times that finite spectra be utilized, that is, a spectra composed of the sum of a finite number of sinusoids.
In accordance with the above background, it is an objective of the present invention to provide an improved musical instrument and method of generating sound which employs an improved digital, non-linear method of producing spectra where the spectra can be finite and the amplitudes of frequency components do not have unwanted limitations.